課程資訊
 課程名稱 實分析一REAL ANALYSIS (I) 開課學期 95-1 授課對象 理學院  數學研究所 授課教師 杜寶生 課號 MATH7201 課程識別碼 221 U2870 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期二5,6(12:20~14:10)星期五5,6(12:20~14:10) 上課地點 新生504 備註 先修高微 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 I.Contents: Part1:Introduction Summability of real numbers. A quick introduction to measure and integration. Part2: Outer measures Measures arising from outer measures, regularity of outer measures, 1-dimensional Lebesgue measure, Caratheodory outer measures, n-dimensional Lebesgue measure and transformation of integrals. Part3: L昌-spaces Completeness of L昌-spaces, Orthonormal systems-completeness and Fourier expansion. Conditional expectation. Part4: Decomposition and Differentiation of Measures Signed measures, The Lebesgue-Radon-Nikodym theorem, Conditional expectation, Differentiation on R明, Functions of bounded variation, Convex functions. II.Course prerequisite: Advanced Calculus, Linear Algebra. III.Reference material ( textbook(s) ): B. R. Gelbaum, Modern Real and Complex Analysis. E. H. Lieb & M. Loss, Analysis. S. Saks, Theory of the Integral. R. L. Wheeden & A. Zygmund, Measure and Integral. IV.Grading scheme: Home work and Mid-term examination each counts 30% Final examination counts 40% V.Others: 課程目標 課程要求 建議先修:Advanced Calculus, Linear Algebra. 評量:Home work and Mid-term examination each counts 30% Final examination counts 40% 預期每週課後學習時數 Office Hours 指定閱讀 參考書目 B. R. Gelbaum, Modern Real and Complex Analysis. E. H. Lieb & M. Loss, Analysis. S. Saks, Theory of the Integral. R. L. Wheeden & A. Zygmund, Measure and Integral. 評量方式(僅供參考)
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